MATH [3D and vectors]

HELLO , This post is about 3D geometry and vectors of class 12

FOR A PDF FOR NOTES OF THE CHAPTER DM ME ON MY INSTAGRAM ACCOUNT AT BOTTOM OF PAGE
TEXT ME VECTORS FOR pdf of vectors and 3D for pdf of 3D

please be patient for reply
send vector for pdf 1 and 3D for pdf 2

S.NO.	topic	format	LINK
1	LIST OF CONCEPTS(Vectors)	WRITTEN	tp1
2	LIST OF CONCEPTS(3D geometry)	WRITTEN	tp2
3	ONE WEEK	WRITTEN	tp3
4	type of question that can be asked	WRITTEN	tp4
5	few examples(NCERT)	WRITTEN	tp5

TOPIC NO. ONE
VECTORS

Basic Concepts of Vectors:

1. Definition of a vector
   
• Scalar and vector quantities
  
• Representation of vectors in 2D and 3D
  
• Types of vectors:
  
• Zero vector
  
• Unit vector
  
• Co-initial vectors
  
• Equal vectors
  
• Collinear vectors
  
• Coplanar vectors
  
2. Operations on Vectors:
   
• Addition of vectors
  
• Subtraction of vectors
  
• Scalar multiplication (Multiplication of a vector by a scalar)
  
• Position vector of a point
  
3. Section Formula:
   
• Internal and external division of a line segment by a vector
  
4. Dot Product (Scalar Product):
   
• Definition and properties
  
• Geometric interpretation of dot product
  
• Angle between two vectors
  
• Applications of dot product:
  
• Work done by a force
  
• Projection of a vector on another vector
  
5. Cross Product (Vector Product):
   
• Definition and properties
• Geometric interpretation of cross product
  
• Area of a parallelogram and triangle
  
• Applications of cross product:
  
• Torque
  
• Moment of a force
  

TOPIC NO. TWO
3D Geometry

Basic Concepts of 3D Geometry:

1. Coordinate System in 3D:
• Cartesian coordinates in 3D space
• Distance formula in 3D
• Section formula in 3D
• Direction cosines and direction ratios
• Angle between two intersecting lines
2. Equation of a Line in 3D:
• Vector form of the equation of a line
• Cartesian form of the equation of a line
• Skew lines, parallel lines, and intersecting lines
• Shortest distance between two skew lines
3. Equation of a Plane:
• Vector form of the equation of a plane
• Cartesian form of the equation of a plane
• Normal form of the equation of a plane
• Intercept form of the equation of a plane
• Angle between two planes
• Angle between a line and a plane
• Condition for parallelism and perpendicularity between planes
4. Distance in 3D:
• Distance of a point from a plane
• Distance between two parallel planes
• Distance between a point and a line
5. Intersection of Line and Plane:
• Point of intersection of a line and a plane
• Condition for a line to lie in a plane
• Condition for the intersection of a line and a plane
6. Coplanarity of Two Lines:
• Condition for two lines to be coplanar

Additional Important Concepts:

1. Projection of Vectors:
• Projection of one vector on another vector
2. Equation of a Plane in Different Forms:
• General form
• Intercept form
• Normal form

TOPIC NO. THREE
one week

Day 1: Introduction to Vectors

Time: 2 hours

Topics:
Basics of vectors: magnitude and direction.
Types of vectors: unit vector, zero vector, equal vectors.
Vector addition, subtraction, and scalar multiplication.
Practice:
Solve basic problems on vector operations from your textbook.
Focus on understanding vector representation and manipulation.
Day 2: Vector Products

Time: 2 hours

Topics:
Dot product (scalar product): Definition, properties, and applications.
Cross product (vector product): Definition, properties, and applications.
Applications of dot and cross products in geometry.
Practice:
Solve problems involving dot and cross products.
Apply these concepts to find angles between vectors and areas of parallelograms.
Day 3: 3D Geometry Basics

Time: 3 hours

Topics:
Cartesian coordinate system in 3D.
Distance formula, section formula, and mid-point formula in 3D.
Direction cosines and direction ratios.
Practice:
Work through examples involving distance and section formulas.
Practice finding direction cosines and ratios for given vectors.
Day 4: Equation of a Line in 3D

Time: 3 houRS

Topics:
Vector form and Cartesian form of a line.
Condition for two lines to be parallel, intersecting, or skew.
Shortest distance between two skew lines.
Practice:
Solve problems involving the equation of a line.
Practice finding the shortest distance between lines.
Day 5: Equation of a Plane in 3D
Time: 3 hours
Topics:
Vector form and Cartesian form of a plane.
Angle between two planes.
Condition for two planes to be parallel or perpendicular.
Distance of a point from a plane.
Practice:
Solve problems on finding the equation of a plane.
Practice calculating the distance of points from planes.
Day 6: Revision and Mixed Practice
Time: 3 hours
Topics:
Review key formulas and concepts from previous days.
Solve mixed problems involving vectors, lines, and planes.
Focus on complex problems that combine multiple concepts.
Practice:
Take up problems from previous year question papers.
Identify and work on weak areas.
Day 7: Final Practice and Clarifications
Time: 2 hours
Activities
Solve a mock test or sample paper covering 3D Geometry and Vectors.
Review mistakes and clarify any remaining doubts.
Go through important points and formulas once more.
Total Time: 18 hours
Tips:
Focus on Understanding: Instead of rote memorization, focus on understanding concepts and their applications.
Practice:
Make sure to practice regularly to reinforce your understanding.
Clarify Doubts: Don’t let doubts linger—resolve them as soon as they arise.

TOPIC NO. four
IMP concepts

Vectors
Objective Type Questions
Multiple Choice Questions (MCQs): Identify the correct vector operation or property.

1. Assertion-Reasoning: Determine the correctness of statements related to vector concepts.

Short Answer Questions

1. Vector Operations: Perform addition, subtraction, or scalar multiplication of vectors.
2. Magnitude of Vectors: Calculate the magnitude of a given vector.
3. Unit Vector: Find the unit vector in the direction of a given vector.
4. Position Vector: Determine the position vector of a point or midpoint of a line segment.

Long Answer Questions

1. Dot Product and Cross Product: Compute the dot product or cross product of two vectors.
2. Projection of a Vector: Calculate the projection of one vector onto another.
3. Collinearity of Vectors: Prove whether given vectors are collinear.
4. Vector Equations of Lines: Derive and solve vector equations of lines.

3D Geometry
Objective Type Questions

1. Multiple Choice Questions (MCQs): Identify the correct equation of a plane or line.

Short Answer Questions

1. Equation of a Line: Derive the equation of a line passing through two points or parallel to a vector.
2. Equation of a Plane: Find the equation of a plane given a point and a normal vector.
3. Distance Between Two Points: Calculate the distance between two points in 3D space.
4. Angle Between Two Vectors or Planes: Determine the angle between two given vectors or planes.

Long Answer Questions

1. Intersection of Line and Plane: Solve for the point of intersection between a line and a plane.
2. Shortest Distance Between Two Skew Lines: Calculate the shortest distance between two skew lines.
3. Angle Between Two Planes: Derive the formula and compute the angle between two planes.
4. Vector and Cartesian Form Conversion: Convert equations from vector form to Cartesian form and vice versa.
5. Problems Involving Direction Cosines and Ratios: Solve problems related to direction cosines and direction ratios.

TOPIC NO. FIVE
SUMS TO TRY BEFORE EXAM

solving this qustion will clear your 99% of concepts in exam there might be a change in value not questions so make sure you solve them wisely and also understand what to think and how to think when such question comes
Vectors (Chapter 10)
Exercise 10.1: Basic Concepts and Operations
Q3,Q5,Q7

Exercise 10.2: Scalar (Dot) Product
Q3,Q6,Q10

Exercise 10.3: Vector (Cross) Product
Q4,Q8,Q12

3D Geometry (Chapter 11)
Exercise 11.1: Direction Cosines and Direction Ratios
Q3,Q7,Q10

Exercise 11.2: Equation of a Line in Space
Q2,Q6,Q8

Exercise 11.3: Equation of a Plane
Q4,Q8,Q11

Exercise 11.4: Coplanarity of Lines
Q3,Q7,Q10

Miscellaneous Exercise on Vectors and 3D Geometry
Q4,Q7,Q12

FOR ANY QUERY DM ME ON INSTAGRAM